diff --git a/pydatastructs/graphs/adjacency_matrix.py b/pydatastructs/graphs/adjacency_matrix.py
index 48e0d3489..a8764de4c 100644
--- a/pydatastructs/graphs/adjacency_matrix.py
+++ b/pydatastructs/graphs/adjacency_matrix.py
@@ -57,12 +57,47 @@ def neighbors(self, node):
         return neighbors
 
     def add_vertex(self, node):
-        raise NotImplementedError("Currently we allow "
-                "adjacency matrix for static graphs only")
+        if node.name in self.matrix:
+            raise ValueError("Vertex %s already exists in the graph." % node.name)
+        self.vertices.append(node.name)
+        setattr(self, node.name, node)
+        self.matrix[node.name] = {}
 
     def remove_vertex(self, node):
-        raise NotImplementedError("Currently we allow "
-                "adjacency matrix for static graphs only.")
+        node = str(node)
+        if node not in self.matrix:
+            raise ValueError("Vertex '%s' is not present in the graph." % node)
+
+        # first we need to remove the edges involving the `node`
+
+        # removing records from dict while iterating over them is tricky
+        # so we'll first identify which edges to remove first
+
+        edges_to_remove = []
+
+        for target in self.matrix[node]:
+            if self.matrix[node].get(target, False):
+                edges_to_remove.append((node, target))
+
+        for source in self.vertices:
+            if self.matrix[source].get(node):
+                edges_to_remove.append((source, node))
+
+        # remove the identified edge weights
+        for source, target in edges_to_remove:
+            edge_key = str(source) + "_" + str(target)
+            self.edge_weights.pop(edge_key)
+
+        self.vertices.remove(node)
+        # eliminate all outgoing edges
+        self.matrix.pop(node, None)
+
+        # eliminate all incoming edges
+        for source in self.vertices:
+            self.matrix[source].pop(node, None)
+
+        if hasattr(self, node):
+            delattr(self, node)
 
     def add_edge(self, source, target, cost=None):
         source, target = str(source), str(target)
diff --git a/pydatastructs/graphs/tests/test_adjacency_matrix.py b/pydatastructs/graphs/tests/test_adjacency_matrix.py
index 2dace4260..7d6e1e4fd 100644
--- a/pydatastructs/graphs/tests/test_adjacency_matrix.py
+++ b/pydatastructs/graphs/tests/test_adjacency_matrix.py
@@ -30,3 +30,23 @@ def test_AdjacencyMatrix():
     assert raises(ValueError, lambda: g.add_edge('v', 'x'))
     assert raises(ValueError, lambda: g.add_edge(2, 3))
     assert raises(ValueError, lambda: g.add_edge(3, 2))
+    assert g.num_vertices() == 3
+    v_3 = AdjacencyMatrixGraphNode(3, 3)
+    g.add_vertex(v_3)
+    assert g.num_vertices() == 4
+    g.add_edge(3, 1, 0)
+    g.add_edge(3, 2, 0)
+    g.add_edge(2, 3, 0)
+    assert g.is_adjacent(3, 1) is True
+    assert g.is_adjacent(0, 2) is False
+    assert g.is_adjacent(1, 3) is False
+    assert g.is_adjacent(2, 3) is True
+    assert g.is_adjacent(3, 2) is True
+    neighbors = g.neighbors(3)
+    assert neighbors == [v_1, v_2]
+    neighbors = g.neighbors(2)
+    assert neighbors == [v_0, v_3]
+    g.remove_vertex(3)
+    neighbors = g.neighbors(2)
+    assert neighbors == [v_0]
+    assert g.num_vertices() == 3